How do I export a blender game to be played within my website?
There is no way to do this.  As described here you can create only Windows, Mac and Linux native applications from BGE.

If you want to create a 3D web application from blender, you should
use a specific addons:


Blend4Web
Verdge3D


Both looks the same, but main difference between them is that Blend4Web uses JavaScript as main scripting tool, Verdge3D uses special block-style logic editor